Context
Carbon nanotubes (CNTs) possess remarkable properties, fundamentally governed by the transition between curvature-induced structural distortions (partial \(\text {sp}^3\) ) and planar ( \(\text {sp}^2\) ) hybridization. We present a detailed computational investigation into the atomic structure of armchair single-walled carbon nanotubes (SWCNTs) with chiral indices (n, n) ranging from (3,3) to (11,11). Using ab initio Hartree-Fock calculations, we precisely quantify a direct, quasi-linear structural transition from increased \(\text {sp}^3\) character to \(\text {sp}^2\) character that is quantitatively dictated by the relief of nanotube curvature (i.e., increasing radius). Our results demonstrate how average bond lengths, bond angles, and dihedral angles regularly evolve as the radius increases, revealing how diminishing curvature drives the progressive convergence toward ideal planar \(\text {sp}^2\) geometry. Crucially, we uncover a noticeable odd-even pattern in the incremental change of radius across the series, indicating precise, localized bond relaxations under strain. These findings provide unprecedented quantitative insights into how fundamental bond parameters dictate hybridization shifts in curved carbon systems, establishing a clearer understanding of the intrinsic flexibility of CNTs for advanced quantum electronics, spintronics, and next-generation materials science.
Methods
The initial geometries of armchair SWCNTs with chiral indices (n, n) from (3,3) to (11,11) were generated using the Avogadro molecular builder. Subsequently, ab initio Hartree-Fock (HF) calculations were performed to fully optimize the geometries using the Gaussian09 software with the 6–31 G basis set. Structural parameters like average bond lengths, bond angles, and dihedral angles were extracted from the optimized structures to quantify the curvature-induced deviations from ideal \(\text {sp}^2\) geometry.
